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A178339
Primes p such that the sum of decimal digits of p divides the product of decimal digits of p+1 and that product is nonzero.
1
11, 13, 17, 211, 233, 277, 367, 431, 457, 523, 541, 547, 587, 727, 743, 761, 853, 857, 1153, 1223, 1373, 1447, 1483, 1531, 1571, 1627, 1663, 1733, 1861, 2141, 2213, 2251, 2273, 2293, 2347, 2383, 2411, 2437, 2473, 2521, 2617, 2657, 2741, 2833, 2851, 3221, 3371
OFFSET
1,1
LINKS
EXAMPLE
2+3+3 = 8 divides 2*3*4 = 24, so 233 is a member.
MAPLE
A178339 := proc(n) option remember: local p, q: if(n=1)then return 11: fi: p:=procname(n-1): do p:=nextprime(p): q:=mul(d, d=convert(p+1, base, 10)): if(q>0 and q mod add(d, d=convert(p, base, 10)) = 0)then return p: fi: od: end: seq(A178339(n), n=1..47); # Nathaniel Johnston, May 27 2011
MATHEMATICA
fQ[n_] := Block[{s = Plus @@ IntegerDigits@n, p = Times @@ IntegerDigits[n + 1]}, Mod[p, s] == 0 && p > 0]; Select[ Prime@ Range@ 250, fQ@# &]; Select[ Prime@ Range@ 500, fQ@# &]
Select[Prime[Range[500]], DigitCount[#+1, 10, 0]==0&&Divisible[Times@@IntegerDigits[ #+1], Total[ IntegerDigits[#]]]&] (* Harvey P. Dale, May 24 2023 *)
CROSSREFS
Sequence in context: A098031 A179208 A098423 * A088561 A211457 A154523
KEYWORD
base,easy,nonn
AUTHOR
Giovanni Teofilatto, May 25 2010
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Jun 05 2010
Name corrected by Nathaniel Johnston, May 27 2011
STATUS
approved